A strong astrophysical constraint on the violation of special relativity
by quantum gravity

T. JACOBSON, S. LIBERATI & D. MATTINGLY

Department of Physics, University of Maryland, College Park, Maryland
20742-4111, USA

Correspondence and requests for materials should be addressed to T.J.
(jacobson@physics.umd.edu).

Special relativity asserts that physical phenomena appear the same to all
unaccelerated observers. This is called Lorentz symmetry and relates long
wavelengths to short ones: if the symmetry is exact it implies that
space-time must look the same at all length scales. Several approaches to
quantum gravity, however, suggest that there may be a microscopic
structure of space-time that leads to a violation of Lorentz symmetry.
This might arise because of the discreteness or non-commutivity of
space-time, or through the action of extra dimensions. Here we determine
a very strong constraint on a type of Lorentz violation that produces a
maximum electron speed less than the speed of light. We use the
observation of 100-MeV synchrotron radiation from the Crab nebula to
improve the previous limit by a factor of 40 million, ruling out this
type of Lorentz violation, and thereby providing an important constraint
on theories of quantum gravity.

What does this mean? In the review article Sean Carroll explains what is
the issue here:

Jacobson et al. consider synchrotron radiation, emitted by electrons
circling in a magnetic field, from the Crab nebula. To produce
high-energy photons through synchrotron emission, the electrons must be
moving close to the speed of light. If Lorentz invariance is violated,
the maximum velocity for photons and for electrons can have a slightly
different value, which imposes a cut-off on the frequency of synchrotron
radiation that can be produced. Using observations of radiation at
frequencies beyond this cut-off, Jacobson et al. are able to set the new
stringent limit on Lorentz invariance. The crucial assumption made in
their analysis is that the behaviour of photons and electrons can be
described by an 'effective local field theory' at low energies. Such
theories are well used in this area of physics, and this seems a
reasonable assumption to make, but exceptions are known. So a window,
albeit small, remains open for Planck-scale effects.

Einstein has been right a lot lately. First with his so-called blunder,
concerning the cosmological constant (now called dark energy) and now
special relativity has held up against new quantum gravity theories.

Variable Speed of Light Now More Unlikely
Update 01/01/2004:The paper referred to this in this article can be found
here.

Lorentz invariance, the theory that space-time is uniform, places
important constraints not only on quantum gravity theory but also on
variability of the speed of light. Varying speed of light theories are
all the rage. But, we have seen earlier this year hard limits to possible
Lorentz invariance violations as I commented on here. Now even harder
limits on Lorentz invariance violations and thus limits on the
variability of the speed of light have been reported by NASA:

A fundamental variation in light speed would violate Lorentz invariance,
the basic principle of special relativity. Such a violation could be a
clue to unification theories. Scientists have hoped to find Lorentz
invariance violations by studying gamma-rays coming from the farthest
reaches of the visible universe, where the quantum foam of space may act
to slow light traveling to us for billions of years.

Stecker looked much closer to home to find that Lorentz invariance is not
being violated. He analyzed gamma-rays from two relatively nearby
galaxies about half a billion light-years away with supermassive black
holes at their centers, named Mkn 421 and Mkn 501. Some of these
galaxies' gamma-rays collide with infrared photons in the universe. These
collisions result in the destruction of the gamma-ray and infrared
photons, as their energy is converted into mass in the form of electrons
and positively charged antimatter-electrons (called positrons), according
to Einstein's famous formula E=mc^2.

Stecker and Glashow have pointed out that evidence of the annihilation of
the highest-energy gamma-rays, obtained from direct observations of Mkn
421 and Mkn 501, demonstrates clearly that Lorentz invariance is alive
and well and not being violated. If Lorentz invariance were violated, the
gamma-rays would pass right through the extragalactic infrared fog with
insufficient energy to cause annihilation.

"The implication is if Lorentz invariance is violated, it is at such a
small level -- less than one part in a thousand trillion -- it is beyond
the ability of our present technology to find," Stecker said. "These
results may also be telling us the correct form of string theory or
quantum gravity must obey the principle of Lorentz invariance."

2003 has been a very good year for Einstein.
Received on Mon Feb 2 11:17:55 2004